Actually, there are loads of places along the East Coast of the U.S. where you could spend days, even weeks, without seeing another boat. Some of the remote inlets along the barrier islands of Virginia's segment of the Delmarva Peninsula, Sand Shoal, New and Metompkin inlets are very quiet, even during the height of boating season.
New Inlet, however, can be a bit hairy to access during a hard, ebb tide because of the nearby shoals and bars. Local knowledge is paramount here. Just beyond the inlet is a small bay that leads to Rattail Creek, which winds for miles through the tidal marsh and averages about 4 feet deep. This is the northernmost range of tarpon, and while I've never been able to catch one here, I have seen dozens rolling in the inlet during ebb tide. These fish are huge, averaging more than 100 pounds.
Sand Shoal inlet is a piece of cake, even when the tide is running. It's wide, very deep and provides access to a vast area of tidal marsh that during high tide, resembles a huge, manicured lawn of sea grasses. It's beautiful, but very buggy. Mostly greenhead flies, skeeters and no see ums, both day and night. You can overcome this with a simple outdoor gazebo screen cover available for under $30 at Wall Mart. This will fit right over your bimini top and provides total protection from the biting critters.
Last October, while traveling down the ICW, there were times when I didn't see another boat for days on end. I was somewhat concerned, mainly because if something were to break down, the ICW in southern Virginia and parts of the Carolinas were nothing more than a winding ditch through a swamp. No people anywhere you looked for miles on end.
Someone mentioned the Florida Keys west of Key West. Been there dozens of times, and most of the time the back country between Mule Key Basin and the Dry Tortugas is devoid of people, but the fishing was fantastic. You could lobster dive at the west end of the Lakes Passage near Boca Grande Key and find all the lobsters you could ever want. It can be a popular sailboat anchorage at times for boats headed to the Tortugas, but most of the time I had the entire place to myself.
The Marquesses Keys are one of the jewels of this area. There are three entrances to the inner area of the Marquesses Keys and Money Harbor, two of which are more than adequate for most sailboats drawing under 6 feet. Both inlets are situated on the south side of the Atoll, but I only recommend entering during high, slack tide. During ebb tide, the water rips through the inlets pretty hard and could slam you into the coral heads nearby. This too is one of those areas where you won't see a soul for days or even weeks on end.
The best attribute of cruising is meeting fellow cruisers. Over the years some of the most fascinating people I've ever encountered have been individuals and couples living aboard their sailboats and trawlers. All that solitude can be nice for a week or two, but beyond that I would much rather be someplace like Boot Key Harbor in Marathon, Florida. I met some fabulous people there, most of which were cruisers, and nearly all were live aboards.
All the best,